(C) The mass per unit length of the chain is $\lambda = \frac{M}{L} = \frac{4\,kg}{2\,m} = 2\,kg/m$.The mass of the hanging part is $m = \lambda \time

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(C) The mass per unit length of the chain is $\lambda = \frac{M}{L} = \frac{4\,kg}{2\,m} = 2\,kg/m$.The mass of the hanging part is $m = \lambda \times \ell = 2\,kg/m \times 0.6\,m = 1.2\,kg$.The center of mass of the hanging part is at a distance of $h = \frac{\ell}{2} = \frac{0.6\,m}{2} = 0.3\,m$ below the edge of the table.The work done $W$ to pull the hanging part onto the table is equal to the change in potential energy of the hanging part,which is $W = mgh = (1.2\,kg) \times (10\,m/s^2) \times (0.3\,m) = 3.6\,J$.

Class 11 Physics Work, Energy, Power and Collision Work Done by Constant Force

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$A$ uniform chain of length $L = 2\,m$ is kept on a table such that a length $\ell = 60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $M = 4\,kg$. The work done in pulling the entire chain onto the table is ............. $J$. (Take $g = 10\,m/s^2$)

A
$12.9$
B
$6.3$
C
$3.6$
D
$2$

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Work, Energy, Power and Collision

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Work Done by Constant Force

$A$ cyclist comes to a skidding stop in $10 \; m$. During this process,the force on the cycle due to the road is $200 \; N$ and is directly opposed to the motion.
$(a)$ How much work does the road do on the cycle?
$(b)$ How much work does the cycle do on the road?

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$A$ body of mass $5\, kg$ is placed at the origin and can move only on the $x$-axis. $A$ force of $10\, N$ is acting on it in a direction making an angle of $60^\circ$ with the $x$-axis and displaces it along the $x$-axis by $4\, m$. The work done by the force is $...\, J$.

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If a force $\vec F = 4\hat i + 5\hat j$ causes a displacement $\vec s = 3\hat i + 6\hat k$,the work done is:

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$A$ force $\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \, N$ acts on an object,causing it to move along the $Y$-axis. If the displacement along the $Y$-axis is $10 \, m$,find the work done by the force in $J$.

Medium

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Given that $W = \vec F \cdot \vec s = 0$ and $F \neq 0, s \neq 0$,then

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$A$ uniform chain of length $L = 2\,m$ is kept on a table such that a length $\ell = 60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $M = 4\,kg$. The work done in pulling the entire chain onto the table is ............. $J$. (Take $g = 10\,m/s^2$)

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$A$ cyclist comes to a skidding stop in $10 \; m$. During this process,the force on the cycle due to the road is $200 \; N$ and is directly opposed to the motion.$(a)$ How much work does the road do on the cycle?$(b)$ How much work does the cycle do on the road?

$A$ body of mass $5\, kg$ is placed at the origin and can move only on the $x$-axis. $A$ force of $10\, N$ is acting on it in a direction making an angle of $60^\circ$ with the $x$-axis and displaces it along the $x$-axis by $4\, m$. The work done by the force is $...\, J$.

If a force $\vec F = 4\hat i + 5\hat j$ causes a displacement $\vec s = 3\hat i + 6\hat k$,the work done is:

$A$ force $\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \, N$ acts on an object,causing it to move along the $Y$-axis. If the displacement along the $Y$-axis is $10 \, m$,find the work done by the force in $J$.

Given that $W = \vec F \cdot \vec s = 0$ and $F \neq 0, s \neq 0$,then

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$A$ cyclist comes to a skidding stop in $10 \; m$. During this process,the force on the cycle due to the road is $200 \; N$ and is directly opposed to the motion.
$(a)$ How much work does the road do on the cycle?
$(b)$ How much work does the cycle do on the road?